Optimal. Leaf size=24 \[ \log \left (3-\frac {e^6}{x \left (9+2 x-\frac {\log (x)}{2}\right )}\right ) \]
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Rubi [F] time = 1.03, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {2 e^6 (17+8 x-\log (x))}{\left (18 x+4 x^2-x \log (x)\right ) \left (54 x+12 x^2-3 x \log (x)+\frac {2 e^6 \left (-18 x-4 x^2+x \log (x)\right )}{18 x+4 x^2-x \log (x)}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\left (2 e^6\right ) \int \frac {17+8 x-\log (x)}{\left (18 x+4 x^2-x \log (x)\right ) \left (54 x+12 x^2-3 x \log (x)+\frac {2 e^6 \left (-18 x-4 x^2+x \log (x)\right )}{18 x+4 x^2-x \log (x)}\right )} \, dx\\ &=\left (2 e^6\right ) \int \frac {-17-8 x+\log (x)}{x (18+4 x-\log (x)) \left (2 e^6-6 x (9+2 x)+3 x \log (x)\right )} \, dx\\ &=\left (2 e^6\right ) \int \left (\frac {1-4 x}{2 e^6 x (18+4 x-\log (x))}+\frac {-2 e^6+3 x-12 x^2}{2 e^6 x \left (2 e^6-54 x-12 x^2+3 x \log (x)\right )}\right ) \, dx\\ &=\int \frac {1-4 x}{x (18+4 x-\log (x))} \, dx+\int \frac {-2 e^6+3 x-12 x^2}{x \left (2 e^6-54 x-12 x^2+3 x \log (x)\right )} \, dx\\ &=-\log (18+4 x-\log (x))+\int \left (\frac {2 e^6}{x \left (-2 e^6+54 x+12 x^2-3 x \log (x)\right )}+\frac {12 x}{-2 e^6+54 x+12 x^2-3 x \log (x)}+\frac {3}{2 e^6-54 x-12 x^2+3 x \log (x)}\right ) \, dx\\ &=-\log (18+4 x-\log (x))+3 \int \frac {1}{2 e^6-54 x-12 x^2+3 x \log (x)} \, dx+12 \int \frac {x}{-2 e^6+54 x+12 x^2-3 x \log (x)} \, dx+\left (2 e^6\right ) \int \frac {1}{x \left (-2 e^6+54 x+12 x^2-3 x \log (x)\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.25, size = 59, normalized size = 2.46 \begin {gather*} 2 e^6 \left (-\frac {\log (x)}{2 e^6}-\frac {\log (18+4 x-\log (x))}{2 e^6}+\frac {\log \left (2 e^6-54 x-12 x^2+3 x \log (x)\right )}{2 e^6}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 35, normalized size = 1.46 \begin {gather*} -\log \left (-4 \, x + \log \relax (x) - 18\right ) + \log \left (-\frac {12 \, x^{2} - 3 \, x \log \relax (x) + 54 \, x - 2 \, e^{6}}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 36, normalized size = 1.50 \begin {gather*} \log \left (-12 \, x^{2} + 3 \, x \log \relax (x) - 54 \, x + 2 \, e^{6}\right ) - \log \left (4 \, x - \log \relax (x) + 18\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.14, size = 230, normalized size = 9.58
method | result | size |
risch | \(-\ln \left (\ln \relax (x )-4 x -18\right )-\ln \relax (2)+\ln \left (-\frac {\ln \relax (x )}{4}+x +\frac {9}{2}\right )+\frac {i \pi \,\mathrm {csgn}\left (i x \left (\frac {\ln \relax (x )}{4}-x -\frac {9}{2}\right )\right ) \left (\mathrm {csgn}\left (i x \left (\frac {\ln \relax (x )}{4}-x -\frac {9}{2}\right )\right )+\mathrm {csgn}\left (i x \right )\right ) \left (\mathrm {csgn}\left (i x \left (\frac {\ln \relax (x )}{4}-x -\frac {9}{2}\right )\right )-\mathrm {csgn}\left (i \left (\frac {\ln \relax (x )}{4}-x -\frac {9}{2}\right )\right )\right )}{2}-6+\ln \left (\frac {2 \,{\mathrm e}^{6} {\mathrm e}^{-\frac {i \pi \mathrm {csgn}\left (i x \left (\frac {\ln \relax (x )}{4}-x -\frac {9}{2}\right )\right )^{3}}{2}} {\mathrm e}^{-\frac {i \pi \mathrm {csgn}\left (i x \left (\frac {\ln \relax (x )}{4}-x -\frac {9}{2}\right )\right )^{2} \mathrm {csgn}\left (i x \right )}{2}} {\mathrm e}^{\frac {i \pi \mathrm {csgn}\left (i x \left (\frac {\ln \relax (x )}{4}-x -\frac {9}{2}\right )\right )^{2} \mathrm {csgn}\left (i \left (\frac {\ln \relax (x )}{4}-x -\frac {9}{2}\right )\right )}{2}} {\mathrm e}^{\frac {i \pi \,\mathrm {csgn}\left (i x \left (\frac {\ln \relax (x )}{4}-x -\frac {9}{2}\right )\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (\frac {\ln \relax (x )}{4}-x -\frac {9}{2}\right )\right )}{2}}}{x \left (-\frac {\ln \relax (x )}{4}+x +\frac {9}{2}\right )}-3\right )\) | \(230\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 44, normalized size = 1.83 \begin {gather*} -{\left (e^{\left (-6\right )} \log \left (-4 \, x + \log \relax (x) - 18\right ) - e^{\left (-6\right )} \log \left (-\frac {12 \, x^{2} - 3 \, x \log \relax (x) + 54 \, x - 2 \, e^{6}}{3 \, x}\right )\right )} e^{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.70, size = 36, normalized size = 1.50 \begin {gather*} \ln \left (54\,x-2\,{\mathrm {e}}^6-3\,x\,\ln \relax (x)+12\,x^2\right )-\ln \relax (x)-\ln \left (4\,x-\ln \relax (x)+18\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.43, size = 39, normalized size = 1.62 \begin {gather*} - \log {\left (\log {\relax (x )} + \frac {- 12 x^{2} - 54 x}{3 x} \right )} + \log {\left (\log {\relax (x )} + \frac {- 12 x^{2} - 54 x + 2 e^{6}}{3 x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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